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Surface Stresses in Solids and its Effect on the Mechanical behavior of Soft Material

Chung-Yuen Hui Field of Theoretical and Applied Mechanics, Dept. of Mechanical and Aerospace Engineering, Cornell University

Elasto-capillarity phenomena – solid deformation driven by liquid surface tension – have been extensively studied, but are distinct from phenomena driven by solid surface stress. A characteristic length scale that describes the deformation of a solid due to surface tension is given by the ratio between the surface stress \sigma_s and elastic modulus (E), \sigma_s/E. For stiff solids such as metals and ceramics, this length is smaller than inter-atomic distances. However, for soft materials such as elastomers and gels with E ranging from tens of Pa to several MPa, \sigma_s/E ranges from tens of nm to hundreds of \mum. Effects of this large value of \sigma_s can be seen in different contexts. In this talk I will give several examples of how surface stresses can act as a significant and even dominant agent in the mechanics of compliant materials such as elastomers and gels. For example, surface stress constraints the faithful reproduction of soft surfaces in replica molding. Experiments and theory have shown that that the adhesion of small hard particles (spheres or cylinders) on soft elastic substrates can be affected by surface stress. Finally, I will give an example on how elastic deformation and surface stresses of the can alter the wetting mechanics of liquid drops on soft elastic substrates. The equilibrium configuration of a liquid drop on a deformable soft substrate is no longer a material property determined by the Young–Dupré equation ; but instead, by two separate conditions : a local balance of interface stresses (Neumann triangle of forces) and configuration energy balance (Neumann triangle of surface energies). I will illustrate the basic idea by considering the wetting of a partially immersed elastic rod.